Representation of Uncertain Multichannel Digital Signal Spaces and Study of Pattern Recognition Based on Metrics and Difference Values on Fuzzy $n$ -Cell Number Spaces

In this paper, we discuss the problem of characterization for uncertain multichannel digital signal spaces, propose using fuzzy n-cell number space to represent uncertain n-channel digital signal space, and put forward a method of constructing such fuzzy n-cell numbers. We introduce two new metrics and concepts of certain types of difference values on fuzzy n -cell number space and study their properties. Further, based on the metrics or difference values appropriately defined, we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment, and we also give practical examples to show the application and rationality of the proposed techniques.

[1]  D. Dubois,et al.  Towards fuzzy differential calculus part 1: Integration of fuzzy mappings , 1982 .

[2]  Sergios Theodoridis,et al.  Pattern Recognition , 1998, IEEE Trans. Neural Networks.

[3]  Chenglin Wen,et al.  On fuzzy n-cell numbers and n-dimension fuzzy vectors , 2007, Fuzzy Sets Syst..

[4]  Jaroslav Ramík,et al.  Canonical fuzzy numbers of dimension two , 1993 .

[5]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[6]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[7]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[8]  Congxin Wu,et al.  Fuzzy n-cell numbers and the differential of fuzzy n-cell number value mappings , 2002, Fuzzy Sets Syst..

[9]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

[10]  Shaocheng Tong,et al.  FUZZY REASONING MODELS AND ALGORITHMS ON TYPE-2 FUZZY SETS , 2008 .

[11]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[12]  Congxin Wu,et al.  The Integral Over A Directed Line Segment Of Fuzzy Mapping And Its Applications , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[13]  Caroline M. Eastman,et al.  Review: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

[14]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[15]  K. Shinkai,et al.  Decision Analysis of Fuzzy Partition Tree Applying Fuzzy Theory , 2007, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[16]  Congxin Wu,et al.  Convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application , 2002, Fuzzy Sets Syst..

[17]  Sergios Theodoridis,et al.  Pattern Recognition, Third Edition , 2006 .

[18]  Osmo Kaleva Fuzzy differential equations , 1987 .

[19]  Ivo G. Rosenberg,et al.  Joint canonical fuzzy numbers , 1993 .

[20]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[21]  Kazuo Nakamura,et al.  Canonical fuzzy numbers of dimension two and fuzzy utility difference for understanding preferential judgments , 1990, Inf. Sci..

[22]  D. Dubois,et al.  Towards fuzzy differential calculus part 3: Differentiation , 1982 .